Stability Analysis Of Fuzzy Cellular Neural Networks Systems

There exists widely the time-delay phenomenon in almost all neural systems. Furthermore, time-delay is usually varying with the change of time. On the other hand, In electronic implementation of neural networks, there exist inevitably time-delays and uncertainties due to the existence of delayed transmission of signals, modeling errors, parametric uncertainties, environment, model reduction and linearization approximations and external disturbances uncertainties, which may influence the stability of the entire network by creating oscillatory or unstable phenomena. Usually, it is much more complicated to analysis the existence of these time-varying delays and uncertainties. Therefore, more values can be obtained from the research into the stability of the uncertain systems.In the paper, the stability and control of fuzzy cellular neural networks with time-varying delays is studied. By using the Lyapunov second method, matrices analysis and linear matrix inequalities, the robust stability, the exponential stability and the asymptotic stability of such neural networks are investigated.In the first chapter, the background of this paper, the state of study in the neural system with time-delay, the main body and the structures of this paper, the three innovation points of this thesis are presented.The second chapter outlines the introduction on the most basic questions that are related to the stability of neural system, the Lyapunov stability theory, the related definition and lemmas and the explanation of symbols.In the third chapter, some new criteria on the global robust stability of fuzzy cellular neural networks with time-varying delays are studied. By combining suitable Lyapunov functional with the matrix inequality technique, the global robust stability of the equilibrium point is deduced.In the forth chapter, some new criteria on the global exponential stability of fuzzy cellular neural networks with time-varying delays are studied. Based on the Lyapunov stability theory and the linear matrix inequality approach, some sufficient condition for the exponential stability for the system are presented. These sufficient conditions are formulated as linear matrix inequalities, which can be solved easily by using LMI toolbox in MATLAB.In the fifth chapter, some new criteria on the global exponential stability of fuzzy cellular neural networks with time-varying delays and variable coefficient are studied. By combining suitable Lyapunov functional with the matrix inequality technique, some sufficient condition for the exponential stability of the system is presented.In chapters 3, 4 and 5, numerical examples are given to demonstrate the effectiveness of the proposed method and illustrate that the results in this paper have a broader scope of application than some existing results in the literature.